Energy factor and mathematical modelling for power DC/DC converters

The mathematical modelling of power DC/DC converters is a historical problem that has accompanied DC/DC conversion technology since the 1940ʹs. Traditional mathematical modelling is not available for complex structure converters because of the very high-order differential equations involved. The authors propose a new model to cover all power DC/DC converters. The energy stored in power DC/DC converters has been much considered in the past. A DC/DC converter behaves in this way because it has some energy storing components. When the converter changes from one steady state to another, the corresponding stored energy changes. Therefore, there must be a transient process from one steady state to the new steady state. The authors have theoretically defined a new concept, namely energy factor (EF), and researched the relationship between it and mathematical modelling for power DC/DC converters. The EF and its associated parameters illustrate the unit-step response and interference recovery which may be helpful for system design and in anticipating DC/DC converter characteristics. Two DC/DC converters are analysed, the Buck converter and the super-lift Luo converter, to demonstrate the application of EF, pumping energy (PE), stored energy (SE), capacitor/inductor stored energy ratio (CIR), energy losses (EL), time constant τ and damping time constant τd.